07-Array Operations Part 2 text: Chapter Overview

Transcription

1 07-rray Operations Part tet: Chapter.-.7 ECEGR 101 Engineering Problem Solving with Matlab Professor Henry Louie Overview Identity Matri Matri Inversion Linear Systems of Equations Element-by-Element Operations Dr. Henry Louie 1

2 Identity Matri Identity matri, I, is the matri equivalent of scalar multiplication by 1 I I I is simply a square matri (number of rows = number of columns) with 1s on the diagonal Dr. Henry Louie Identity Matri Built-in function to create the Identify Matri is the size of the matri Dr. Henry Louie

3 Inverse of a Matri Matri B is an inverse of if *B=B*=I. To find an inverse of, use the inv function. and B have to be square. Notation: -1. Dr. Henry Louie 5 Inverse of a Matri Dr. Henry Louie 6

4 Inverse of a Matri: Determinant Conditions for the eistence of an inverse: has to be square, Its determinant must be nonzero. a a 11 1 a a 1 det a a a a To calculate the determinant, use the MTLB function det. Dr. Henry Louie 7 Inverse of a Matri: Determinant Dr. Henry Louie 8

5 System of Linear Equations B B 1 B B B B B B 1 X B Dr. Henry Louie 9 System of Linear Eqs. How can we solve X=B? -1 X= -1 B IX= -1 B X= -1 B solution equivalent to X = \B Dr. Henry Louie 10 5

6 System of Linear Eqs. How can we solve XC=D? XCC -1 =DC -1 XI=DC -1 X=DC -1 solution equivalent to X = D/C Used infrequently! Dr. Henry Louie 11 Solve the following system of linear equations: 1 + = = 5 Dr. Henry Louie 1 6

7 Solve the following system of linear equations: 1 + = = 5 Dr. Henry Louie 1 Element-By-Element Operations Carried out on each array element separately: multiplication:.* eponent:.^ right division:./ left division:.\ Dr. Henry Louie 1 7

8 Element-By-Element Operations Calculates values of the function y= -9 for integer between 1 and 10. Dr. Henry Louie 15 Create the following arrays: = [1 5]; and y = [ ]; What operation do you have to perform to get as the result [ ]? Dr. Henry Louie 16 8

9 Create the following arrays: = [1 5]; and y = [ ]; What operation do you have to perform to get as the result [ ]? >>.*y ans = Dr. Henry Louie 17 ssume that a, b, c, and d are following epressions? a) a + b b) a.* b c) a * b d) a * c e) a + c f) a + d g) a.* d h) a * d Dr. Henry Louie 18 9

10 ssume that a, b, c, and d are following epressions? a) a + b Dr. Henry Louie 19 ssume that a, b, c, and d are following epressions? b) a.* b Dr. Henry Louie 0 10

11 ssume that a, b, c, and d are following epressions? c) a * b Dr. Henry Louie 1 ssume that a, b, c, and d are following epressions? d) a * c Dr. Henry Louie 11

12 ssume that a, b, c, and d are following epressions? e) a + c Dr. Henry Louie ssume that a, b, c, and d are following epressions? f) a + d Dr. Henry Louie 1

13 ssume that a, b, c, and d are following epressions? g) a.* d Dr. Henry Louie 5 ssume that a, b, c, and d are following epressions? h) a * d Dr. Henry Louie 6 1

14 ssume that a, b, c, and d are following epressions? h) a * d Dr. Henry Louie 7 If C and F are Celsius and Fahrenheit temperatures, respectively, the formula for conversion from Celsius to Fahrenheit is F = 9C/5 +. Use vector operations to compute and display the Fahrenheit equivalent of Celsius temperatures ranging from 0 to 0 in steps of 1. Dr. Henry Louie 8 1

15 >> C = 0:1:0 C = >> F = 9*C/5 + F = Columns 1 through Columns 8 through Dr. Henry Louie 9 Compute z given the following values for b, c and n: b = c = 10 n = [1 5] b z c n Dr. Henry Louie 0 15

16 Compute z given the following values for b, c and n: b = c = 10 n = [1 5] >> b = ; c = 10; n = 1:5; b z c n n b >> z = b.^n z = 8 16 [1 5] [ 1 5 ] >> z = b.^n/c z = Dr. Henry Louie 1 Compute z given the following values for b, c and n: b = c = [1 5] n = b z c n Dr. Henry Louie 16

17 Compute z given the following values for b, c and n: b = c = [1 5] n = >> b = ; c = 1:5; n = ; b z c 8 [1 5] >> z = b^n./c z = n >> z = b^n/c??? Error using ==> mrdivide Matri dimensions must agree. Dr. Henry Louie Compute z given the following values for b, c and n: b = [1 5] c = 10 n = b z c n Dr. Henry Louie 17

18 Compute z given the following values for b, c and n: b = [1 5] c = 10 n = >> b = 1:5; c = 10; n = ; >> b.^n ans = [1 5] b z c [1 n 5 ] >> z = b.^n/c z = Dr. Henry Louie 5 18